The erythrocyte membrane is modelled as a two dimensional viscoelastic continuum that evolves under the application of stress. The present analysis on the erythrocyte membrane is motivated by the recent development of knowledge on its molecular structure and by its complex behavior exhibited in dynamic micropipette testing and in tank treading during shear flow. The proposed constitutive equations have the form similar to that of a two dimensional Kelvin model with a constant area condition. However, the membrane viscosity is made to depend on the rate of strain and the elastic strain tensor is measured from the evolving preferred configuration. The constitutive equations proposed in the present analysis explain in a consistent manner the data on both the deformation and recovery phases of the micropipette experiment. The rheological equations of the present study are applied in a later section to the analysis of a plane membrane deformation that is quantitatively similar to the tank-treading motion of the erythrocytes in a shear field. The computations yield useful information on how the membrane viscosity becomes a more dominant feature in tank-treading motion. The present model reflects the microstructure of the erythrocyte membrane. A membrane composed of a lipid bilayer may be idealized as a viscous membrane with a constant area condition. The network of protein molecules embedded in and attached to the lipid bilayer of the erythrocyte membrane serves as a storage medium for the elastic strain in the membrane. The molecular organization of this network evolves continuously during a prolonged deformation. The material constants appearing in the proposed constitutive equations may be useful indicators of the biochemical state of the membrane in health and disease.